This invention relates to the evaluation of uncertainty, in particular, a method for evaluating uncertainty in measurements carried out by measuring equipment. The invention also relates to computer programs for carrying out said method and a computer programmed system containing said computer programs, a system for measuring and evaluating uncertainty associated with said measurement.
Calibration of measurement equipment and testing of products are commonly carried out by calibration and testing laboratories, as well as manufacturing companies to assess conformity to measurement standards, including but not limited to international standards, such as ISO/IEC guides and standards. On the other hand, calibration and testing laboratories are audited by laboratory accreditation systems to assess for conformity to ISO/IEC 17025 standard (ISO/IEC 17025—General requirements for the competence of testing and calibration laboratories).
As a requirement to conform to ISO/IEC 17025, accredited testing and calibration laboratories and in-house laboratories of manufacturing companies are required to evaluate uncertainty in their measurement result or calibration result, and to include such uncertainty evaluation in the test results or the calibration certificates that accompanies the products.
In principle, measurement uncertainty is associated with the result of a measurement that defines the range of values that could reasonably be attributed to the measured quantity. When expressed in a specific form, uncertainty is indicated by the level of confidence that the value of the measured quantity lies within a range defined by an uncertainty interval. In real life, any measurement is subject to imperfections and errors (both systematic and random). This means that a measurement is incomplete without an estimation of the uncertainty associated with the measurement. Accordingly, a measurement result should be accompanied by an estimation of its uncertainty so that a user can tell how accurately the measurement result represents the true value of the measured quantity, or the user can assess the reliability of the result in comparison with reference values or results from different sources.
In accordance with the ISO standards, errors can be fundamentally divided into two categories, namely, random errors and systematic errors. Random errors, such as random fluctuations of temperature, humidity and air-pressure, would affect to the measurement result randomly. Systematic errors, such as measurement instrument's circuit insulation, resolution, could be estimated either from physical theory, technical specification of measurement equipment, manufacturer's manual or long time observed data of equipments. In the course of a measurement, errors arise due to factors that influence the outcome of a measurement. For example, resistance measurements carried out in an environment where temperature fluctuates may give rise to large variations in the measured value of resistance.
Effects of random errors can be evaluated by repeated measurement results, while effects of systematic errors can be estimated from extensive experience in metrology, technical specification of measurement equipment, manufacturer's manual or long time observed data of those equipments.
Accordingly, the uncertainty in the value of a measurand is generally arrived at based on several mathematical components. These components may be grouped into two categories according to the way in which their numerical value is estimated. Those which are evaluated by statistical methods are classified as type A, and those which are evaluated by other means are classified as type B. The final report of uncertainty should contain a complete list of all the components and specify for each component the method used to obtain its numerical value.
Over the years, different mathematical procedures have been developed for calculating measurement uncertainty. To provide a basis for the international comparison of measurement results, the Guide to the Expression of Uncertainty in Measurement (GUM) was published by ISO in 1993 and has since been widely accepted for a wide range of measurements among many countries. As a technical requirement of ISO/IEC 17025, uncertainty evaluation is recommended to be executed based on ISO-GUM.
U.S. Pat. No. 6,640,607 discloses a method and apparatus for calibrating measuring machines. To manage uncertainty in measurement using measuring machines, this method is capable of achieving automated calibration, in contrast to the previous ones which perform calibration by a skilled worker. To achieve automated calibration, the patent discloses the steps of positioning a reference measuring machine previously calibrated and an object measuring machine to be calibrated in such a manner that a measurement space by the reference measuring machine is superimposed on a measuring space by the object measuring machine; acquiring first measurement values from the object measuring machine and second measurement values from the reference measuring machine; and calibrating the object measuring machine based on the first and second measurement values.
In Japanese patent 2002-267436 A, a method of estimating uncertainty of coordinate measurement of one point is proposed. The method estimates the uncertainty of coordinate measurement of a calibrated coordinate measurement machine (CMM) based on the uncertainty of length measurement of said calibrated CMM. In particular, the method addresses problems associated with modelling the behaviour of uncertainty in a CMM.
The Danish Technological Institute developed a software named “GUM Workbench” for the calculation of measurement uncertainty. This software supports calculation of statistical treatment of uncertainty evaluation based on ISO-GUM. However, the software does not include a function which would enable it to be associated with physical measurement equipments to support measurement. Therefore, GUM Workbench cannot be used for high-end national laboratories research level. However, it is not suitable for practical use in testing and calibration laboratories or manufacturing industries.
Other approaches for uncertainty evaluation exist as well. For example, S. D. Phillips et al. [1] propose a method for calculating measurement uncertainty using prior information. Bayesian inference is used to include prior information about the value of the measurand in the uncertainty calculation. Another approach by V. J. Barwick et al. [2] aims at the estimation of the uncertainty associated with recovery particularly in relation to analytical chemistry. In addition, M. G. Cox and P. M. Harris [3] present software specifications for uncertainty evaluation according to ISO-GUM.
Despite the development of methods for evaluating uncertainty and its implementation by many parties, most methods involve mainly the mathematical or statistical treatment for uncertainty evaluation of measured value. None of above methods, software and equipments explains sources of uncertainty quantity by quantity. Besides, sources of uncertainty vary from one particular measurement system to another, and can only be identified from experience. Existing methods do not adequately take such sources of uncertainty into consideration in the mathematical evaluation.
Accordingly, it is an object of the present invention to propose, clarify and evaluate uncertainties source by source and finally reach the uncertainty evaluation budget table. It is an additional object of the present invention to provide a system which is suitable for practical uncertainty evaluation in testing and calibration laboratories and manufacturing industries.